11-coding-backpropagation-without-keras-tf.ipynb

{
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import math\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# input\n",
        "input = np.array([\n",
        "    [1,1],\n",
        "    [1,0],\n",
        "    [0,1],\n",
        "    [0,0],\n",
        "])\n",
        "\n",
        "# output\n",
        "target = np.array([1,0,0,0])"
      ],
      "metadata": {
        "id": "f7xjpZmhM6PG"
      },
      "execution_count": 84,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# config\n",
        "num_input = 2\n",
        "num_hidden = 5\n",
        "num_output = 1\n",
        "\n",
        "# sigmoid func\n",
        "def sigmoid(x):\n",
        "  return 1/(1 + math.exp(-x))\n",
        "\n",
        "sig = np.vectorize(sigmoid)"
      ],
      "metadata": {
        "id": "lNBgbkuMPjAs"
      },
      "execution_count": 85,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# initialize weight and bias\n",
        "\n",
        "b_hidden = np.random.uniform(low=-3, high=3, size=(num_hidden))\n",
        "w_hidden = np.random.uniform(low=-3, high=3, size=(num_input, num_hidden))\n",
        "\n",
        "print('w_hidden:', w_hidden)\n",
        "print('b_hidden:', b_hidden)\n",
        "print('\\n')\n",
        "\n",
        "b_output = np.random.uniform(low=-3, high=3, size=(num_output))\n",
        "w_output = np.random.uniform(low=-3, high=3, size=(num_hidden, num_output))\n",
        "\n",
        "print('w_output:', w_output)\n",
        "print('b_output:', b_output)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4PBVj_KJQyTK",
        "outputId": "c792855b-004b-4d17-9350-a27d9cfb3948"
      },
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "w_hidden: [[-1.30103586  1.72216717 -1.50226785  0.09372265  1.05485678]\n",
            " [ 2.18515416  2.00876974 -2.61415131 -1.08520796  1.74629174]]\n",
            "b_hidden: [-2.87651981 -0.69018596  1.7570895   1.63948399 -1.07253688]\n",
            "\n",
            "\n",
            "w_output: [[-0.9354688 ]\n",
            " [-0.41668922]\n",
            " [ 1.59585998]\n",
            " [-0.26768599]\n",
            " [ 1.05975709]]\n",
            "b_output: [0.42784752]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# loss and accuracy\n",
        "loss_values = []\n",
        "acc_values = []\n",
        "\n",
        "lr = 0.5\n",
        "epochs = 50\n",
        "\n",
        "for epoch in range(epochs):\n",
        "  MSE = 0\n",
        "  new_target = np.zeros(4)\n",
        "\n",
        "  for idx, inp in enumerate(input): # feedforward\n",
        "    # hidden layer\n",
        "    o_hidden = np.matmul(input[idx], w_hidden) + b_hidden\n",
        "    o_hidden = sig(o_hidden)\n",
        "\n",
        "    # print('----------------')\n",
        "    # print(f'input[{idx}]:', input[idx], 'w_hidden:', w_hidden, 'b_hidden:', b_hidden)\n",
        "    # print('o_hidden:', o_hidden)\n",
        "    # print('\\n')\n",
        "\n",
        "    # output layer\n",
        "    o_output = np.matmul(o_hidden, w_output)\n",
        "    o_output = sig(o_output)\n",
        "\n",
        "    # print('o_hidden', o_hidden, 'w_output:', w_output, 'b_output:', b_output)\n",
        "    # print('o_output:', o_output)\n",
        "    # print('\\n')\n",
        "\n",
        "    # count error\n",
        "    error = target[idx] - o_output\n",
        "    MSE += (error*error)\n",
        "\n",
        "    new_target[idx] = o_output.round()\n",
        "    eh = error @ w_output.T # error hidden\n",
        "\n",
        "    # print('error', error)\n",
        "    # print('eh', eh)\n",
        "    # print(f'new_target[{idx}]:', new_target[idx])\n",
        "    # print('\\n')\n",
        "\n",
        "\n",
        "    # backpropagation (using formula for sigmoid func)\n",
        "    w_output = w_output + (lr * (error * o_output * (1 - o_output)) * o_hidden[np.newaxis].T)\n",
        "    b_output = b_output + (lr * (error * o_output * (1 - o_output)))\n",
        "\n",
        "    w_hidden = w_hidden + (lr * (eh * o_hidden * (1 - o_hidden)) * input[idx][np.newaxis].T)\n",
        "    b_hidden = b_hidden + (lr * (eh * o_hidden * (1 - o_hidden)))\n",
        "\n",
        "  MSE = MSE/4\n",
        "  acc = 1 - (np.sum(np.absolute(target - new_target))/4)\n",
        "\n",
        "  loss_values.append(MSE)\n",
        "  acc_values.append(acc)\n",
        "\n",
        "  print('epoch:', epoch, '|', 'error:', MSE, 'acc:', acc)\n",
        "  # print('----------------')\n",
        "  # print('\\n')\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rdI9h9stQ1vy",
        "outputId": "102c1ce1-8424-4f20-8c37-28b4124ed22d"
      },
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "epoch: 0 | error: [0.39279193] acc: 0.25\n",
            "epoch: 1 | error: [0.32836246] acc: 0.5\n",
            "epoch: 2 | error: [0.28392941] acc: 0.25\n",
            "epoch: 3 | error: [0.25476702] acc: 0.5\n",
            "epoch: 4 | error: [0.23502926] acc: 0.5\n",
            "epoch: 5 | error: [0.22080964] acc: 0.75\n",
            "epoch: 6 | error: [0.2098476] acc: 0.75\n",
            "epoch: 7 | error: [0.20084739] acc: 0.75\n",
            "epoch: 8 | error: [0.1930478] acc: 0.75\n",
            "epoch: 9 | error: [0.18599245] acc: 0.75\n",
            "epoch: 10 | error: [0.17940854] acc: 0.75\n",
            "epoch: 11 | error: [0.17314031] acc: 0.75\n",
            "epoch: 12 | error: [0.16710914] acc: 0.75\n",
            "epoch: 13 | error: [0.16128619] acc: 0.75\n",
            "epoch: 14 | error: [0.15567142] acc: 0.75\n",
            "epoch: 15 | error: [0.15027724] acc: 0.75\n",
            "epoch: 16 | error: [0.14511685] acc: 0.75\n",
            "epoch: 17 | error: [0.14019774] acc: 0.75\n",
            "epoch: 18 | error: [0.13551938] acc: 0.75\n",
            "epoch: 19 | error: [0.13107393] acc: 0.75\n",
            "epoch: 20 | error: [0.12684831] acc: 0.75\n",
            "epoch: 21 | error: [0.12282643] acc: 0.75\n",
            "epoch: 22 | error: [0.11899113] acc: 0.75\n",
            "epoch: 23 | error: [0.11532559] acc: 0.75\n",
            "epoch: 24 | error: [0.11181411] acc: 0.75\n",
            "epoch: 25 | error: [0.10844258] acc: 0.75\n",
            "epoch: 26 | error: [0.1051986] acc: 0.75\n",
            "epoch: 27 | error: [0.10207152] acc: 1.0\n",
            "epoch: 28 | error: [0.09905224] acc: 1.0\n",
            "epoch: 29 | error: [0.0961331] acc: 1.0\n",
            "epoch: 30 | error: [0.09330765] acc: 1.0\n",
            "epoch: 31 | error: [0.09057053] acc: 1.0\n",
            "epoch: 32 | error: [0.08791722] acc: 1.0\n",
            "epoch: 33 | error: [0.08534395] acc: 1.0\n",
            "epoch: 34 | error: [0.08284751] acc: 1.0\n",
            "epoch: 35 | error: [0.08042518] acc: 1.0\n",
            "epoch: 36 | error: [0.07807462] acc: 1.0\n",
            "epoch: 37 | error: [0.07579377] acc: 1.0\n",
            "epoch: 38 | error: [0.07358078] acc: 1.0\n",
            "epoch: 39 | error: [0.07143399] acc: 1.0\n",
            "epoch: 40 | error: [0.06935185] acc: 1.0\n",
            "epoch: 41 | error: [0.06733289] acc: 1.0\n",
            "epoch: 42 | error: [0.06537571] acc: 1.0\n",
            "epoch: 43 | error: [0.06347895] acc: 1.0\n",
            "epoch: 44 | error: [0.06164125] acc: 1.0\n",
            "epoch: 45 | error: [0.05986129] acc: 1.0\n",
            "epoch: 46 | error: [0.05813773] acc: 1.0\n",
            "epoch: 47 | error: [0.05646924] acc: 1.0\n",
            "epoch: 48 | error: [0.05485447] acc: 1.0\n",
            "epoch: 49 | error: [0.05329207] acc: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plot1 = plt.figure(1)\n",
        "plt.plot(loss_values)\n",
        "plt.show()\n",
        "\n",
        "plot2 = plt.figure(2)\n",
        "plt.plot(acc_values)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 843
        },
        "id": "7GkqCIzcRk6H",
        "outputId": "db2107c3-4a7d-48b2-8533-9292189a135b"
      },
      "execution_count": 88,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}